Cutoff profiles for quantum Levy processes and quantum random transpositions

• 成果类型: Article
• 署名作者: Freslon, Amaury; Teyssier, Lucas; Wang, Simeng
• 署名单位: Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); University of Vienna; Harbin Institute of Technology
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-022-01121-4
• 发表日期: 2022
• 页码: 1285-1327
• 关键词: random-walks; permutation; semigroups; LAWS

摘要

We consider a natural analogue of Brownian motion on free orthogonal quantum groups and prove that it exhibits a cutoff at time N ln(N). Then, we study the induced classical process on the real line and compute its atoms and density. This enables us to find the cutoff profile, which involves free Poisson distributions and the semicircle law. We prove similar results for quantum permutations and quantum random transpositions.